To complete what's said above.. If your boat (galley, caravel, galleon, transports are the only ones - in the epic game - that can transport ground units. and nuclear submarines that can transport tactical nukes too, same rules apply).
Either you have the boat and the unit in the same city, select the unit and press L to load it in the boat, or have the boat right next to the coast, move the unit next to the boat, and load it in by moving it in the boat. I don't use the mouse, I usually use the keypad/arrows to move units, and it works well to load units in boats.
also note the transport capacity, galleys = 2, etc
To unload:
move the ship next to a coastal square, and either:
1) right-click the ship and select the unit you want to unload
2) right-click the ship and click on "wake transported (x)" where x shows you how many units are being transported
3) using the arrow/keypad keys, "move" the ship on the coast square. Of course ships can't go on it, but a window will appear asking you which unit you want to unload ("nevermind" "all" etc)
For aircraft carriers, use the relocation command of the bombers/fighters/etc (shift-R to move one, or J to move a whole stack of airplanes) then click on the carrier.
I think that covers it all
